The visualization of a local electric field has been expected to give an important clue in the evaluation of performances or functions or a trouble analysis of a solid device, a CNT (carbon nanotube) transistor, a light emitting element, an electron emission element which constitutes a nano structural body or, to be more specific, a trouble diagnosis analysis of an LSI or the evaluation of performances or functions or a trouble analysis of a defect of a gate portion or the like.
As a method for visualizing a local electric field whose importance is increasing in the development and the analysis of such a nano structural body, there has been proposed a local electric field visualizing method which uses a scanning transmission electron microscope (STEM) (non-patent document 1). FIG. 11 is a conceptual view of such a method. An anode is arranged to face a conductive probe having a pointed tip end in an opposed manner, and when a voltage is applied to the anode, an extremely strong local electric field is induced on the tip end of the probe. When the probe is electrically conductive, the whole probe has the same potential. When the probe is placed in an electric field, that is, even when a potential gradient is present in a space, it is necessary to set the same potential to the whole probe. Accordingly, an apparent charge is induced in the tip end of the probe so that the potential of the probe is adjusted such that the whole probe has the same potential. That is, due to this apparent charge, a local electric field which is an extremely strong electric field is formed in the vicinity of the tip end of the probe to which the potential is applied. When a primary electron beam of the scanning transmission electron microscope passes through this strong local electric field, an orbit of the primary electron beam is largely deflected. That is, the deflection of the orbit of the primary electron beam is considered as the scattering where an electron orbit is deflected due to a Coulomb force between a point charge induced on the tip end of the probe and the primary electron beam, that is, is considered as Rutherford scattering.
Accordingly, in a transmission image of the scanning transmission electron microscope, electron beams are scattered and are deflected from an electron beam detector (STEM detector) mounted on a lower portion of a casing so that a detection signal is not generated in a region where the scattering occurs, thereby a black region appears surrounding the distal end of the probe.
In the Rutherford scattering, an electron draws a hyperbolic orbit. An orbit from infinity approximates a point charge with a fixed distance b (impact parameter). Thereafter, the orbit is bent and deflected due to a Coulomb interactive force between the electron and the point charge. Here, the impact parameter b is expressed by a following formula.
  b  =            1              4        ⁢                  πɛ          0                      ⁢                            z          1                ⁢                  e          2                            mv        2              ⁢    cot    ⁢          θ      2      
In the formula, e indicates an elementary charge, z1e indicates an apparent point charge induced on a tip end of a probe, m indicates an electron mass, δ0 indicates a dielectric constant in vacuum, v indicates velocity of a primary electron beam, and θ indicates a scattering angle.
As a result of such scattering, the orbit of the primary electron beam is deflected to the outside of the electron beam detector so that the black shadow is formed. By extracting a completely black portion of an image, that is, a black portion of a level equal to brightness which imparts blackness of the probe or the electrode, a region subjected to the deflection to an extent that the scanning electron is completely displaced to the outside of the electron beam detector is specified. It is needless to say that contrast and brightness can be arbitrarily adjusted in the scanning transmission electron microscope, and it is a premise that a darkest portion of a bright field image is not saturated.
From a black region on the tip end of the probe observed when the distal end of the probe and the anode are arranged with a gap of 10 μm as shown in FIG. 12(a) and a potential of 258V is applied to the anode, brightness of a level equal to the brightness of the probe is extracted. As a result, a white circular region shown in FIG. 12(b) is formed. All primary electron beams incident within the circular region are displaced to the outside of the electron beam detector, and a radius 1.5 μm of circular region at this point of time becomes the impact parameter b. The scattering angle θ is determined based on a radius of the electron beam detector and a distance between the electron beam detector and the tip end of the probe, and an electric field E on a boundary of the circular region is expressed by a following formula.
  E  =                    mv        2            eb        ⁢    tan    ⁢          θ      2      
The electron field E is expressed by a following formula when the primary electron beam of low acceleration outside the application of relativity theory is used.
  E  =                    2        ⁢        V            b        ⁢    tan    ⁢          θ      2      
Here, V indicates an acceleration voltage of the primary electron beam.
A scattering angle can be obtained based on the use of such relationship formula due to the size of the black shadow which appears due to scattering of electrons so that the intensity of a local electric field at an edge of the shadow can be obtained.
Non-patent Document 1: J. Fujita et al. “In-situ Visualization of Local Field Enhancement in an Ultra Sharp Tungsten Emitter under a Low Voltage Scanning Transmission Electron Microscope” Jpn. J. Appl. Phys. 46 (2007) 498-501